Spectral Action in Noncommutative Geometry

What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral appro...

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Bibliographische Detailangaben
1. Verfasser: Eckstein, Michał (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:1st ed. 2018.
Schriftenreihe:SpringerBriefs in Mathematical Physics, 27
Schlagworte:
Physics.
Mathematical physics.
Elementary particles (Physics).
Quantum field theory.
Gravitation.
Algebraic geometry.
Harmonic analysis.
ISBN:9783319947884
ISSN:2197-1757 ;
Online-Zugang: Volltext
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Inhaltsangabe:
  • Preface
  • The dwelling of the spectral action
  • The toolkit for computations
  • Analytic properties of spectral functions
  • Fluctuations of the spectral action
  • Open problems
  • Classical tool from geometry and analysis
  • About "heat operators
  • Definition of pdos, Sobolev spaces and a few spectral properties
  • Complex parameter-dependent symbols and parametrix
  • About e-t P as a pdo and about its kernel
  • The small-t asymptotics of e-t P
  • Meromorphic extensions of certain series and their residues
  • Examples of spectral triples
  • Spheres
  • Tori
  • Noncommutative tori
  • Podle ́s sphere
  • Index. .

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